Dual Nature of Particle de-Broglie Hypothesis:
In 1924, Louis de Broglie suggested that matter exhibit dual behaviour i.e. both particle and wave nature. This means that it has both momentum and wavelength. According to de Broglie, the wavelength associated with a particle of mass ‘m’, moving with a velocity ‘v’ is given by equation:
λ = h/mv where h = Planck’s constant
This equation is applicable to all material objects but it has significance only in case of microscopic particles. According to Planck’s quantum theory.
E = hv or hc/λ
Where h = Plank’s constant, v = frequency of wave According to Einstein equation.
E = mc2
Where, m = mass of photon c = velocity of light, Equating both, we get,
hv = mc2 but v = c/λ
hc/λ = mc2 or λ = \(=\frac{h}{m c} \text { or } \lambda=\frac{h}{m v}\)
The above equation is de Broglie equation.
